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1.1.8 Tutorial: polynomial rings, use command
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When you want to do a computation in CoCoA-5, the first thing you
need to do is tell CoCoA-5 in which ring to compute. The
use
command informs CoCoA-5 about this. The most convenient method does
two things at once: it creates the polynomial ring, and then chooses
that ring as the "current ring".
Once the correct current ring has been selected, you may type in
polynomials using a natural syntax; note that you must use
*
to
denote all products (e.g. between coefficients and indeterminates,
or even between powers of indeterminates).
The most common coefficient fields are the rationals (denoted by
QQ
)
and small prime finite fields (denoted by
ZZ/(p)
).
/**/ use P ::= QQ[x,y]; // polys in x,y with coefficients in QQ
/**/ (x+y)^2;
x^2 + 2*x*y + y^2
/**/ use ZZ/(2)[a,b]; // polys in a,b with coefficients in ZZ/(2)
/**/ (a+b)^2;
a^2 + b^2
/**/ use QQ[x,y,z],lex; // polys in x,y,z, coeffs in QQ, term order "lex"
/**/ x+y^2;
x + y^2
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